Gemara

41b (Rav Papa): Whenever the Torah requires a Tefach, this is the width of four thumbs, which equals the width of six pinkies or five intermediate (index) fingers.

67a: It says "Arisoseichem" twice. We expound as if it said 'Isaschem'. Chalah applies to the Shi'ur of 'your dough' (in the Midbar, everyone received an Omer (the volume of 43 and a fifth eggs) of Man each day);

87b - Question (Rami bar Chama): Do we divide Chavitim in half by hand, or with a Kli?

Answer (Rav Chisda): Surely, it is by hand. If a Kli were required (for exactness), a scale would be required! (It is most exact.)

Suggestion: Perhaps a scale is required!

Rejection: One of the curses is that people (will share an oven to save fuel, the bread will break inside, and they) will weigh the (pieces of) bread with a scale (to ensure that each receives the proper amount). This shows that it is improper to do so.

Pesachim 109a (Rav Chisda): The Revi'is mid'Oraisa is the volume of a box two thumbs by two thumbs by two and seven tenths thumbs:

Eruvin 4a (R. Chiya bar Ashi): Shi'urim are a tradition from Moshe from Sinai.

Question: R. Yosi b'Ribi Chanina expounded "Eretz Zeis Shemen" - most Shi'urim of Eretz Yisrael are the size of an olive.

Answer: They are a tradition from Sinai. The verse is an Asmachta.

83a: Rebbi measured and found that k'Beitzah (regarding Tum'ah) is an egg and excess, i.e. another one part in 20 for each egg.

Kelim 17:6 (Mishnah): K'Beitzah (for Tum'as Ochlim) is not a big or small egg, rather, average;

R. Yehudah says, we take the biggest and smallest eggs, put both in a Kli full of water, and half of what spills out is k'Beitzah;

R. Yosi says, who knows what is the biggest and smallest?! Rather, it depends on the observer's opinion.

Rishonim

Rambam (Hilchos Bikurim 6:15): A Revi'is is the volume of a box two fingers by two fingers and 2.7 fingers tall. The Shi'ur Chalah is about a box 10 (fingers) by 10 by three and a ninth fingers, which equals a cube six and seven ninths fingers on each side. This is 43.2 eggs. This is the weight of 68 and two thirds Sela'im of wheat flour of Mitzrayim, which weighs 520 Mitzri Zuz nowadays.

Rambam (Hilchos Sefer Torah 9:9): The thickness of a thumb for all Shi'urei Torah is an average finger. We found that it is seven barley seeds pressed next to each other, which is like the length of two barley seeds with space.

Rambam (Hilchos Chametz 5:12): The Shi'ur of Chalah is 43.2 eggs, like average eggs, not like its weight.

Magid Mishneh: This is clear, for the weight and volume of eggs are not the same.

Perush ha'Mishnayos (Chalah 2:6): The Shi'ur of Chalah was not given in weight, rather, in volume. One who gives the Shi'ur in weight errs blatantly, unless he approximates based on a certain species.

Chazon Ish (Mo'ed 39:4): If a Shi'ur was said in length, it was given for Chachamim to fix and individuals to estimate only in length. Likewise, a Shi'ur of weight may be fixed and estimated only in weight. It follows that the Shi'ur changes with nature. If Chachamim said what is the weight of the Shi'ur of flour or a Revi'is, this is not a Shi'ur Torah. Perush ha'Mishnayos (Chalah 2:6) alludes to this. He permits giving a weight based on wheat flour of a certain city for this year, if it is known to be uniform, to help to clarify the Shi'ur Torah.

Mishneh Halachos (8:194): Ba'al ha'Itur (Aseres ha'Dibros Hilchos Matzah u'Maror) says that we do not rely on weight for the Shi'ur for Chalah. Some wheat is less dense than other wheat.

Poskim

Shulchan Aruch (YD 324:1): The Shi'ur for Chalah is flour that fills a measure that holds 43.2 eggs. This amount of wheat flour of Mitzrayim weighs 520 Drahams.

Shach (2): I estimated that this is slightly less than three quarts.

Kaf ha'Chayim (456:6): One may not rely on such measures, for they change over time and in different places. Every Gadol in his generation must gauge based on his time and place.

Bedek ha'Bayis: Orchos Chayim says that one should add two and a quarter eggs. One should add to all the Shi'urim the amount for Kituf (smoothing the dough). Women normally leave over flour for Kituf. If one started with an exact Shi'ur, it will lack the Shi'ur!

Kaf ha'Chayim (7): The Roke'ach says to use 44 eggs, for we cannot be exact about what are average eggs. Perush ha'Mishnayos (Kelim 17:6) rules like R. Yosi, who says that it depends on how it looks to the observer.

Pischei Teshuvah (1): The Tzlach says that one should bless only if there are 86 eggs. Hanhagos ha'Gra says similarly.

Rema: The Shi'ur Chalah is about a box 10 by 10 by three and a ninth fingers, which equals a cube six and seven ninths fingers on each side. These fingers are thumb-widths.

Tzlach (Pesachim 116b DH v'Ho'il): The eggs found nowadays are about half the size that they were in the early days when Chachamim estimated (Shi'urim). The Shi'ur for Chalah is 43.2 eggs. The Tosfos Yom Tov measured that this is the old pint of Prague. I found that it is less. I made a Kli seven thumbs less two ninths long in each dimension, which is the Shi'ur for Chalah (YD 324, based on the calculation for the size of a Mikveh). This Kli holds two pints! This is a contradiction in the Shi'ur for Chalah. This Shi'ur and for Mikveh are both traditions from Sinai. We must say that either thumbs became bigger than they were in the days of the Tana'im, or eggs became smaller. It is known that the generations are getting smaller; we cannot say that our thumbs are bigger than those in the days of the Gemara, so we must say that the eggs are smaller. Therefore, I say that one should take Chalah from a pint of flour without a Berachah. I do not suggest to be more lenient than the Shi'ur of the Tosfos Yom Tov. I say to bless only if there are a bit more than two pints. A k'Zayis is like an egg nowadays. One should use this for Matzah, Maror and all Shi'urei Torah.

Chasam Sofer (1:127): I measured fingers of average sized people, and there were seven barley seeds to a thumb, like in the days of the Rambam. I made a Kli that holds 311 and third fingers (like the Rambam says). It held 15 Austrian Zeidels, and 43.2 eggs put into a full Kli of water displaced seven Zeidles and a fraction, about half as much. Also the weight was half what it should be. Teshuvah me'Ahavah (YD 324) says that we cannot learn from the Tzlach's limbs, for he was tall. This is wrong, for I measured (and found like the Tzlach). The fingers did not change. In another Teshuvah (181) I wrote that even though Chachamim knew that the generations are changing, every generation gauges according to thumbs at the time. Presumably, everything else will change correspondingly, e.g. the Amah. The Chavos Ya'ir (in Chut ha'Shani) said so, but he says that an egg is more than two by two fingers (by 2.7 fingers, the size of a Revi'is). Perhaps Chazal, including the regions of the Rambam, Rif and perhaps all Sefardim, had bigger chickens. Where they have a tradition, they eat them. Recently, in our country were found Perl Heiners (turkeys? - PF) which have signs of Kashrus, but we do not eat them due to tradition. Perhaps they are Dores, just like swamp-chickens, or there are Tamei species that resemble it. Their eggs are bigger than chicken eggs. However, it is astounding that Gedolei Ashkenaz, e.g. the Roke'ach, Rosh, Tur, Mordechai, Maharil, R. Yerucham, and all the more so the Acharonim such as the Tosfos Yom Tov and Eliyahu Rabah (did not mention a discrepancy in the measures). How could such a great change could occur in such a small time, and only in eggs, but not in barley or the height of man!

Kaf ha'Chayim (456:11): When measuring thumbs, one should not press it down, for this makes it wider.

Yismach Levav (OC 8 DH v'Hinei): Pesach ha'Dvir says that the Tzlach's measurement was based on a large man, pressing the thumb. If we average the size of the thumbs of a big and small man, without pressing, there is no discrepancy.

Kaf ha'Chayim (12): Our eggs in Yerushalayim weigh a sixth less than the Rambam's calculation. 43.2 eggs of our eggs weigh only 430 Drahams. One should separate Chalah from this amount without a Berachah. We bless only on the full Shi'ur of 520 Drahams.

Chazon Ish (Mo'ed 39:1): It seems that R. Yosi agrees that if we could know what is the biggest and smallest, he would agree! Why does he say to estimate? Perhaps one will err! Rather, Shi'urim are based on one's estimation, just like one estimates to take Terumah. The tradition from Sinai for Shi'urim was based on man's estimation. Chachamim fixed the Shi'ur for Yisrael, e.g. to say that 'k'Zayis' refers to Aguri (a certain species of olive), barley refers to what grows in the Midbar, etc. If Chachamim did not fix the Shi'ur, or if what was fixed is not found, again everyone uses his own estimation.

Ohr l'Tziyon (3, introduction, Shi'urei Mitzvos 2): Pesach ha'Dvir (190) says that even though the primary measurement is volume, when the weight is the same, one may rely on the weight. Avkas Rochel said not to rely on the weight only when it is unlike the volume. In our generation weight is better, lest people err about estimating the size of an average thumb. Beis David warns not to rely on 520 Drahams for clean Soles (fine flour, and bless on separating Chalah from it). It is denser than regular flour; it is a Berachah l'Vatalah. Many Sefardi Gedolim from the Rambam until our times confirmed that the Shi'urim are the same. Gedolei Ashkenaz who did not use the Draham assumed that it changed. Nowadays we see that a thumb is two centimeters, and based on this a Revi'is is 27 Drahams, like the Rambam says. Even the Chazon Ish would agree that Sefardim follow our tradition, that the measures did not change. The Gemara says that a man is three Amos tall. The Ramban and Rashba say that that this is from head to toe. Tosfos and the Rambam hold that this is from shoulder to toe. Based on these two opinions, the thumb is 2.4 centimeters (like the Chazon Ish says) or two centimeters, respectively. We find Sefardi Gedolim who were stringent for the larger Shi'ur (and considered a thumb to be 2.5 centimeters) for Mikveh, the four Minim and Sukah. This is because we are stringent about a Torah Safek. Almost everything else is mid'Rabanan, so we rely on our tradition. Nowadays, Chalah is mid'Rabanan. We eat two k'Zeisim of Matzah, which is more than the stringent Shi'ur of a k'Zayis. Kidush over wine is mid'Rabanan.

Teshuvos v'Hanhagos (5:129): Perush ha'Mishnayos (Eduyos 1:2) says that a Revi'is of water weighs 27 Drahams. Nowadays a Draham is 3.2 grams, so a Revi'is of weighs 86.4 grams, and its volume is 86.4 milliliters. If so, the Shi'ur of Chalah (43.2 eggs) is about 2.5 liters. Flour is about half as dense as water, so it weighs 1.25 kilos. The custom in Yerushalayim is to take Chalah from this weight without a Berachah. Some are stringent for 1.2 kilos (perhaps the flour is less dense than average - PF). The Chazon Ish holds that a Revi'is is 150 milliliters; he must hold that in the days of the Rambam, the Draham weighed more. 'Shi'ur ha'Revi'is (if R. Yehudah Margolin) said that we found old Drahams, and they are only 2.8 grams. If so, a Revi'is is only 75 milliliters. According to this, an Amah is 46 centimeters. Indeed, this is the size of an average Amah nowadays. This also causes the weight of our barley to equal what the Rambam says. If so, one should separate Chalah from 1080 grams. The Brisker Rav was stringent for a kilo. It is good to be stringent also regarding the Isur to make a dough for Matzah larger than Shi'ur Chalah.

Note: According to the Chazon Ish, the Shi'ur Chalah is 4.32 liters. If flour is half as dense as water, this amount of flour weighs 2.16 kilos. Perush ha'Mishnayos (Eduyos 1:2) says that flour is two thirds as dense as water. I found that it is almost 60% as dense as water - PF.

Piskei Teshuvos (457:1): Leket ha'Omer (Rav Bloy), Hilchos Chalah (5(8)) says that according to R. Chaim Na'eh, one separates Chalah if there are 1.25 kilos of flour, but blesses only if there are 1.67 kilos. According to the Chazon Ish, one separates if there are 1.2 kilos of flour, but blesses only if there are 2.25 kilos.